A task from kinematics

1. The problem statement, all variables and given/known data
The human organism can handle acceleration that is 4 times bigger than gravitational acceleration. What is the smallest radius of curvature that can handle pilot of an airplane that files with constant speed of 1000 km/h?

2. Relevant equations
This task seems easy but I don't have idea what to do. All I know is if the pilot is flying with constant speed then tangential acceleration is zero and if we are talking about the minimal radius then radial acceleration must be maximal which means that ar=4•g.

3. The attempt at a solution
I tried like this ar= v2/r and then rmin=v2/ar=1966,40m
And the result is 0.25•1011m
There is obviously something I couldn't think of. I'd like someone to give me idea what to do. Thanks :)

The 0.25 x 1011 m is obviously wrong: the radius of the earth is 6 x 106 m and planes do fly around with such speeds without killing the passengers.

I don't see anything wrong with your 1970 m, except one thing: the earth keeps pulling with 1 times g as well. So if the loop is vertical, the driver experiences 5 g at the bottom and 3 at the top. Not good. If the circle is horizontal, 1 g and 4 g add up vectorially to √17 times g, also > 4 g. So I would feel safer in your plane if ar = √15 g (But it's a small correction and I wonder if that is asked for in your exercise)

By the way, if your given data is only in one digit, it is better to round off your results a little bit: so 4g corresponds to a circle with a radius of 1970 m
(personally I would even prefer 2 km, but teacher may think different).

The 0.25 x 1011 m is obviously wrong: the radius of the earth is 6 x 106 m and planes do fly around with such speeds without killing the passengers.

I don't see anything wrong with your 1970 m, except one thing: the earth keeps pulling with 1 times g as well. So if the loop is vertical, the driver experiences 5 g at the bottom and 3 at the top. Not good. If the circle is horizontal, 1 g and 4 g add up vectorially to √17 times g, also > 4 g. So I would feel safer in your plane if ar = √15 g (But it's a small correction and I wonder if that is asked for in your exercise)

By the way, if your given data is only in one digit, it is better to round off your results a little bit: so 4g corresponds to a circle with a radius of 1970 m
(personally I would even prefer 2 km, but teacher may think different).